Didier Drogba's first-half goal was enough to extend Chelsea's lead at the Premiership summit to 11 points.
Drogba was on target after 25 minutes, turning in Damien Duff's cross after good work by Frank Lampard.
It was a rare moment of joy for Drogba, who otherwise had a nightmare evening, missing a host of chances as Chelsea dominated relegation strugglers Albion.
Albion's only threat was a shot from Kanu after 73 minutes that was headed to safety by Robert Huth.
Chelsea coach Jose Mourinho drafted in Huth and Drogba for Ricardo Carvalho and Mateja Kezman - but the changes did nothing to disturb the Premiership pace-setters' smooth rhythm.
Eidur Gudjohnsen headed wide inside the opening seconds after John Terry flicked on Duff's corner.
Albion striker Geoff Horsfield had the ball in the net twice in the first 14 minutes, but both times the strikes were clearly offside.
Drogba wasted a good chance after 22 minutes when he raced clear, but his lob was weak and was easily blocked by on-rushing Albion goalkeeper Russell Hoult.
But there was no escape for Albion three minutes later as Drogba opened the scoring with a wonderfully-constructed goal.
Lampard released Duff on the left flank and his cross was delivered perfectly for Drogba to provide a simple finish.
Drogba almost extended Chelsea's lead after 32 minutes when he was through on goal again, but his touch was poor and Albion survived.
Albion had barely troubled Chelsea, and their first attempt on goal came three minutes before the interval, a tame shot by Kanu that was easily claimed by goalkeeper Petr Cech.
Drogba's finishing was wayward, and he was guilty of another bad miss after 62 minutes when he was released by Lampard. He had time and space on the edge of the area, but steered his finish wastefully wide.
The striker's evening was, at best, very mixed, and he was the culprit again when he somehow failed to hit the target with a header from only eight yards after a perfect cross from Joe Cole.
And Chelsea almost paid the price for Drogba's poor finishing after 71 minutes when Huth had to head Kanu's goal-bound drive to safety.
Chelsea: Cech, Paulo Ferreira, Terry, Huth, Gallas, Makelele, Cole (Kezman 86), Lampard, Duff (Smertin 90), Gudjohnsen (Jarosik 74), Drogba.
Subs Not Used: Ricardo Carvalho, Cudicini.
Goals: Drogba 26.
West Brom: Hoult, Robinson, Gaardsoe, Clement, Albrechtsen, Gera, Richardson (Greening 86), Wallwork, Horsfield (Earnshaw 83), Campbell, Kanu.
Subs Not Used: Scimeca, Moore, Kuszczak.
Ref: N Barry (N Lincolnshire).